Traditional dynamic pricing addresses the problem of finding a pricing policy that maximizes a function of the revenue (typically, its expected value) under inventory constraints. Depending on the assumptions regarding the demand model and one's knowledge about it, the pricing policy then will seek to set prices so that the seller sells the right amount of units at the right time, at least as far as revenue maximization is concerned. This understanding of dynamic pricing, also known as “revenue management,” is motivated by the problems in the airline and hotel industry that initiated this field of research and is typically concerned with the following setting: a seller wants to price a fixed total capacity C of a perishable (i.e. a resource that is not depleted over time [see reference 6]), such as seats in an airplane, and a price-sensitive demand Dt(Pt), where Pt denotes the price of the resource at time t and t ranges from 0 to the time horizon H (e.g. the moment the corresponding airport check-in counter closes). The problem of revenue management is then stated as that of selecting an offering policy, denoted by the tuple {(qt,pt)}t of units offered and price points over a horizon so that the cumulative revenue is maximized while making sure that the available capacity is exhausted at t=H [see references 4 and 6]. In many applications, it is assumed that qt=Dt(pt) so the decision variables are only the prices {pt}t.
The systems and methods disclosed herein provide a computationally efficient method for performing dynamic pricing.